Point source solutions and coupling parameters in cratering mechanics

The use of a point source of an impactor energy and momentum to replace the effects of the impactor is examined. The general framework and notation of the impact cratering problems are described; it is determined that the cratering phenomena are governed by Froude, Cauchy, and Reynolds numbers. The coupling parameter concept is defined mathematically as the measure that governs limit point source solutions. Examples of cases where coupling parameters are used are presented. The relationships of the coupling parameter concept with steady flow and the Z-model of cratering of Maxwell (1973, 1977) are studied. Crater size, ejecta distributions, growth histories, time of formation, melt volume, and shock decay for various scale factors for impact cratering mechanics are calculated, and the applicability of the coupling parameter to the study of cratering mechanics is revealed.